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Game Theory A little knowledge is a dangerous thing. So is a lot. - Albert Einstein Topic 7 Information.

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Presentation on theme: "Game Theory A little knowledge is a dangerous thing. So is a lot. - Albert Einstein Topic 7 Information."— Presentation transcript:

1 Game Theory A little knowledge is a dangerous thing. So is a lot. - Albert Einstein Topic 7 Information

2 Strategic Use of Information Incentive Schemes Creating situations in which observable outcomes reveal the unobservable actions of the opponents. Screening Creating situations in which the better-informed opponents observable actions reveal their unobservable traits. Mike Shor 2

3 Signaling Definition Using actions that other players would interpret in a way that would favor you in the game play Requires It is not in the best interest for people to signal falsely Implies signaling must be costly! Mike Shor 3

4 Auto Insurance A $1,000 deductible? High risk drivers: 30% chance of claim Risk aversion: willing to pay $500 Low risk drivers: 10% chance of claim Risk aversion: willing to pay $200 Mike Shor 4

5 Pooling vs. Separating A pooling equilibrium has all types taking the same action Therefore, cannot distinguish types by the actions they take A separating equilibrium has different types taking different actions Therefore, can distinguish types by the actions they take Mike Shor 5

6 Cost of No Deductible If the cost of avoiding a deductible is Less than $200 Both types buy Pooling Equilibrium Greater than $500 Neither type buys Pooling equilibrium Between $200 and $500 Only high risk drivers buy Separating equilibrium Mike Shor 6

7 Pooling Insurance company charges $200 Both types buy Expected profit for insurance company: High risk drivers: $200 - (30%) $1,000 = $200 - $300 = -$100 Low risk drivers: $200 - (10%) $1,000 = $200 - $100 = $100 Profitable only if there are more low-risk drivers than high-risk drivers Mike Shor 7

8 Separating Insurance company charges $500 Only high-risk drivers buy Expected profit for insurance company: High risk drivers: $500 - (30%) $1,000 = $500 - $300 = $200 Low risk drivers:$0 Always profitable Mike Shor 8

9 Comparing Equilibria Imagine that p proportion are high-risk Insurance company charges $200 Profit: $100 (1-p) - $100 p = $100-$200p Insurance company charges $500 Profit: $200p Compare: $200p > $100-$200p p > ¼ better to separate than pool Mike Shor 9

10 Self-Selection Only high risk drivers self-select into the contract to buy insurance Screening sets up the proper incentives for individuals to self-select Pooling has the danger of adverse selection Mike Shor 10

11 Adverse Selection Imagine ½ of the population are high- risk drivers Insurance company calculates expected cost of not having a deductible: (1/2) (10%) $ (1/2) (30%) $1000 = $200 Add a 10% profit, charge $220 Only high risk drivers sign up! Mike Shor 11

12 How to Screen Want to know an unobservable trait Identify an action that is more costly for bad types than good types Ask the person (are you good?) But… attach a cost to the answer Cost high enough so bad types dont lie Low enough so good types dont lie Mike Shor 12

13 Screening Education as a signaling and screening device Is there value to an economics degree? Imagine not: no effect on productivity, but is observed by employers Cost of economics major varies Mike Shor 13

14 Example: Econ majors How hard should an econ major be? Two types of workers: High and low quality NPV of salary high quality worker:$900,000 low quality worker:$700,000 Disutility per econ credit high quality worker:$4,000 low quality worker:$6,000 Mike Shor 14

15 High Quality Workers If I get an econ major: Signal I am a high quality worker Receive $900,000 - $4,000 N If I dont get an econ major Signal I am a low quality worker Receive $700, ,000 – 4,000 N> 700, ,000 > 4,000 N 50 credits> N Mike Shor 15

16 Low Quality Workers If I get an econ major: Signal I am a high quality worker Receive $900,000 - $6,000 N If I dont get an econ major Signal I am a low quality worker Receive $700, ,000 – 6,000 N< 700, ,000 < 6,000 N 33 credits< N Mike Shor 16

17 Screening To achieve a separating equilibrium: Costly enough to deter low types Not so costly as to deter high types High reward – high-type cost – low-type cost > Low reward < Low reward Mike Shor 17

18 Screening To achieve a separating equilibrium: High types work for high reward Low types accept low reward High reward – Low reward – Low reward > high-type cost < low-type cost Mike Shor 18

19 Screening Solves Market Imperfections Market for lemons (used cars) Worth between $1000 and $3000 to buyers Worth $200 less to sellers Only seller knows true value Buyer offers $2,000 Adverse selection Only cars between $1,000 and $2,200 sold Buyer offers $1,600 Adverse selection Only cars between $1,000 and $1,800 sold Market equilibrium price: $1,200 Only worst 20% of cars are ever sold Mike Shor 19

20 Screening Solves Market Imperfections Market for lemons What about introducing a screen? Extended warranty Cheaper to provide for good cars than bad cars Other examples Coupons Banks made of granite Mike Shor 20

21 Hiding from Signals The opportunity to signal may prevent some types from hiding their characteristics Examples: Financial disclosures GPA on résumé Taking classes pass / fail Mike Shor 21

22 Hiding from Signals Suppose students can take a course pass/fail or for a letter grade. An A student should signal her abilities by taking the course for a letter grade – separating herself from the population of Bs and Cs. This leaves Bs and Cs taking the course pass/fail. Now, B students have incentive to take the course for a letter grade to separate from Cs. Ultimately, only C students take the course pass/fail. If employers are rational – will know how to read pass/fail grades. C students cannot hide! Mike Shor 22

23 Summary Enticing high effort is hard work Leakages Global vs. individual incentives Rewarding the right people Screening Identify unobservable cost differences Exploit them (carefully) Mike Shor 23


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